Mathematics, 04.02.2020 16:48 macyfrakes

The equation of the line passing through the ordered pair (a,0) and parallel to the line x + 2y = 7 is.

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Answer from: rwlockwood1

The equation of the parallel line is x + 2y = a

Step-by-step explanation:

* lets revise the general form of the linear equation

- The general form of the linear equation is ax + by + c = 0, where

a , b , c are real numbers

- The linear equation represented by a line its slope = -a/b and

intersects the y-axis at point (0 , -c/b) means y-intercept = -c/b

- The parallel lines have equal slopes and different y-intercepts

* Now lets solve the problem

- There is a line with equation x + 2y = 7

- Put the equation in the general form

∵ x + 2y = 7 ⇒ subtract 7 from both sides

∴ x + 2y - 7 = 0

∵ ax + by + c = 0 is the general form of the linear equation

∴ a = 1 , b = 2 , c = -7

∵ The slope of the line is -a/b

∴ The slope of the line -1/2

- We need to find the equation of the parallel line which has the

same slope

∵ The two lines are parallel

∴ Their slopes are equal

∴ The slope of the line is -1/2

∵ The slope depends on a and b

∴ The line has the same value of a and b

∵ a = 1 and b = 2

∵ ax + by + c = 0

∴ The equation of the line is x + 2y + c = 0

- To find c substitute x and y in the equation by the coordinates of

any point on the line

∵ The line passing through point (a , 0)

- Substitute x by a and y by 0

∴ a + 2(0) + c = =

∴ a + c = 0 ⇒ subtract a from both sides

∴ c = -a

- Substitute the value of c in the equation by - a

∴ The equation of the line is x + 2y - a = 0 ⇒ add a for both sides

∴ The equation of the line is x + 2y = a

* The equation of the parallel line is x + 2y = a

- They are equal in slopes and different in y-intercepts

Answer from: Quest

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Answer from: Quest

the answer to this question is 3/19

step-by-step explanation:

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